Application of DSO algorithm for estimating the parameters of triple diode model-based solar PV system

Solar Photovoltaic (SPV) technology advancements are primarily aimed at decarbonizing and enhancing the resiliency of the energy grid. Incorporating SPV is one of the ways to achieve the goal of energy efficiency. Because of the nonlinearity, modeling of SPV is a very difficult process. Identification of variables in a lumped electric circuit model is required for accurate modeling of the SPV system. This paper presents a new state-of-the-art control technique based on human artefacts dubbed Drone Squadron Optimization for estimating 15 parameters of a three-diode equivalent model solar PV system. The suggested method simulates a nonlinear relationship between the P–V and I–V performance curves, lowering the difference between experimental and calculated data. To evaluate the adaptive performance in every climatic state, two different test cases with commercial PV cells, RTC France and photo watt-201, are used. The proposed method provides a more accurate parameter estimate. To validate the recommended approach's performance, the data are compared to the results of the most recent and powerful methodologies in the literature. For the RTC and PWP Photo Watt Cell, the DSO technique has the lowest Root Mean Square Error (RMSE) of 6.7776 × 10–4 and 0.002310324 × 10–4, respectively.

the basic performance indicators of the system.Precise and reliable estimation of intrinsic parameters are the prerequisites for implementing an accurate equivalent circuit model.The data provided by the manufacturer in the Datasheet do not reveal complete information of all the intrinsic variables.Estimating accurate information on all intrinsic variables under any climatic condition is the scope of this work.These intrinsic variables change with perturbation in radiation, temperature soiling effects, aging factor, and partial shading 10 .
Most of the researchers in the literature diverted their focus to meta-heuristic methods due to promising results.The solution is obtained either by adopting naturally inspired algorithms, artifacts, or evolutionary techniques.Nature-inspired algorithms generally mimic the phenomena occurring in the nature Wind driven optimization (WDO), Flower Pollination Algorithm (FPA), Grasshopper Optimization Algorithm(GOA), Simulated Annealing (SA), Evaporation-based Water Cycle algorithm (ERWCA), Wind-driven optimization(WDO) [11][12][13][14][15][16] , while artifact mimics the human intelligence JAYA algorithm, Imperialistic competitive algorithm (ICA), Brain Storming Algorithm (BSA), Drone Squadron Optimization (DSO), Artificial Immune System (AIS), Bio geography-based Optimization (BBO), Harmony Search (HS), Teaching Learning Based Optimization (TLBO) with modifications have evolved [17][18][19][20][21][22][23][24] .Recently Meta heuristic approaches have been used extensively for parameter extraction due to their accuracy and fast computing capability.Researchers have tried to improve the performance by combining multiple algorithms to get the best optimal solution referred to as hybrid algorithms.
An effective parameter estimation method with a hybrid Whale Optimization Algorithm, combined with particle swarm optimization.To improve exploitation capability with reduced range.The error was found to be minimal.WOA adopts the behavior of humpback whales and the searching approach of birds involves PSO exponential function-based PSO with the inertial weight adopted to overcome the problems associated with premature convergence problems 19 .Bacterial foraging optimization involves a greater number of parameters with more computational time 25 .Lambert's function with heuristic adopting differential evolution is proposed to achieve better convergence with a significant reduction in computation time 26 .Mimicking the reproduction behavior of bonobos an optimization algorithm named Bonobo Optimizer (BO) is proposed to demonstrate the efficiency of adopting fusion and fission mechanisms.Bonobos adopt various mating strategies to exploit multidimensional search space to avoid local trapping of the solution.Hence there is an adaptive change in population size 27 .Gradient-based optimization with Eagle Strategy is used to enhance efficiency and robustness.
This paper also evaluates dynamic PV models such as integral and fractional PV solar models.Both static and dynamic models are analyzed to obtain the optimal results 28 .GWO is inspired by food-searching behavior practiced by grasshoppers within the boundary with two different life stages, namely lava for slow exploitation and insect stage for dynamic exploration of the search space 13 .To improve accuracy and reliability, a new change with enhancement in the evolutionary operator is presented using an enhanced Roa-1 algorithm 29 .This approach achieves adaptive population size with a linear minimization strategy.Despite all these algorithms, no single method achieves the least root mean square error considering adaptive climatic conditions for three diode model.

Three diode modelling by using fifteen parameters
There are various models available for performance analysis of solar cells.Modeling of solar cells can adopt singlediode, two-diode, and three-diode approaches.The simplest one-diode model is easy to analyze with compromise in terms of accuracy.Two diode approach is widely used in the literature to extract the parameters it seeks the help of numerical techniques for a few variable extraction and the remaining parameters are estimated using optimization algorithms to reduce complexity.In this manuscript, 3-diode modeling of PV cells is discussed to extract 15 parameters using drone squadron optimization.Here, Fig. 2 presents the 3-diode model of a PV cell consisting of three diode currents I D1 , I D2, and I D3 .R sh and R s denote the shunt and series resistances respectively.The photo-generated current is represented by I ph , I PV is the output current available to the load and V PV is the voltage measured across the shunt resistance.
Equations to compute output current and photo-generated current under specified irradiation and temperature are given in Eq. (1) and (2).From Eq. (3), T is the temperature K is Boltzmann constant, G is irradiation Where a is the ideality factor, Gref and Tref is the temperature and Irradiance at Standard Test Condition (STC) respectively, Eg is the band gap and q is charge of the electron.From (1), it is evident that there are 15 parameters which are identified as I 01ref , I 02ref , I 03ref , I ph ref , a 1 , a 2 , a 3 , L Rp , L Rs , K Rs , K Rp , K i , , R 1pRef , R s1Ref and R s2Ref .These intrinsic variables exactly determine the performance characteristics of the PV module.Under varying climatic conditions, the open circuit voltage and short circuit current can be determined using the following equation.These intrinsic variables exactly determine the performance characteristics of the PV module.Under varying climatic conditions, the open circuit voltage and short circuit current can be determined using the following Eq's, (1) where N is the experimental data, I i is the experimental value and I iext denotes the estimated value from 15 parameter extraction.Estimating the parameters for one set of climatic conditions enables the user to predict the power versus voltage (P-V) and current versus voltage (I-V) curves for all weather conditions.This detailed model adapts, despite any variation in radiation and temperature as the intrinsic variables are free to change.This flexibility is not accounted for in classical models available in the literature.On modeling SPV, the precise value obtained by this approach aids in deducing the P-V and I-V curves at varying weather conditions.This enables the industrialist to design a reliable and efficient inverter for any specified location 30 .

Problem formulation
Global optimization problems are generally derivative-free approaches with no assumptions.A global, autoadaptive hyper-heuristic algorithm inspired by human Invented drones that can evolve on their own partially.The firmware inside these drones enables the researcher to change the mechanism rather than depending on the bio-inspiration 20 .Despite natural behavior mimicking procedures such as particle swarm optimization.This method inculcates the recombination by varying the solution with a unique procedure to act as a revolutionary approach.In the vast search space, the drones are free to move to explore and exploit the search space.This technique does not inculcate the pre-coded algorithm during its movement, it synthesizes its code to move in a search space.DSO optimization algorithm consists of four major components where the complete task of estimation is carried out.The command center is the most intelligent part where the orders to execute and return drone to the destiny are done by modifying and updating the codes inside the firmware.The perturbation is denoted by P which is the sum of departure and offset.The firmware only produces a trial coordinate (TC) by a perturbation process called biased random walk.This TC is obtained by calculating P. Two arrays are formed, namely current Best and Global Best.
where C1 is the constant defined by the user, G the Gaussian distribution, U is the uniform distribution, and D is one of the variables in the objective function which is defined as 15 in this modeling CBC and GBC are current best coordinates and global best coordinates respectively.Offset generally returns the amount of perturbation, thus updation of trial coordinates are computed based on this perturbation function which is denoted by (P).Search space can be shrinked based on departure coordinates which helps to locate the neighboring points.
Reference perturbation initializes perturbation to optimize and improve the search performance.Drone movement stage, the target positions are computed automatically by exploring and exploiting search space using various mechanisms Depending on the choice of recombination trial coordinates, the direction of the drone is fixed to one particular direction.To avoid biasing a correction factor is introduced and the violation limits are perturbed.Firmware update, here, team quality is computed for each iteration to update the rank and violation.The Command Center updates firmware by considering the best and worst by following the rules 20 .
Here, UB and LB are upper and lower-bound objective function arrays, and TmC is an array of 2D team coordinates.This violation limit for each team of drones is given in Eq. ( 15).This violation in each case, for all the drones are considered with the updation of the firmware at the command center accordingly.The stagnation detection and next iteration procedures are repeated until the optimal results are achieved.The flow chart mimicking the pseudo-code is represented in Figs. 3 and 4. It is evident that the root mean squared error estimated for these two cells are 6.7776 × 10 -4 and estimated for these two cells are 6.7776 × 10 -4 and 0.231032 × 10 -3 respectively, which is the least on par with results available in the literature 39 .

Results analysis
This manuscript proposes a novel DSO-based adaptive algorithm to validate the performance and accuracy of three diode PV model.Two different cases are analyzed to demonstrate accuracy and reliability.In case one, the validation of the proposed approach is carried out considering two commercial PV cells, namely RTC France cell (10)    1.The 15 parameters estimated for the 3-diode model using DSO for two commercial PV cells algorithms are tabulated in Table 2.It is evident that the root mean squared error estimated for these two cells are 6.7776 × 10 -4 and 0.231032 × 10 -3 respectively, which is the least on par with results available in the literature 39 .The graphical analysis of RTC France and Photo Watt PWP-201 for PV and IV curves using the DSO algorithm are presented in Figs. 5, 6, 8, and 9.The estimated values coincide with the practical experimental values and hence it exhibits minimum deviation accounting for low RMSE.Figures 7 and 10 show the best objective function with various statistical analysis metrics such as current best, global best, current mean, median, and average for different no of iterations.For each run, the best solution is estimated which is illustrated in Fig. 11.For the RTC France cell the least RMSE of 6.8 × 10 -4 is obtained with minimal iteration as depicted in the Fig. 8.        noting that DSO outperformed all other optimization approaches in terms of attaining the lowest RMSE and fastest execution time while maintaining a strong convergence response.The last row of the table clearly reports the superiority of DSO over other techniques.The low value of RMSE at different temperatures is made bold in Table 3, along with 15 Parameters five other parameters of the module are also estimated to improve the accuracy of the modelling.In case two, the DSO approach has been implemented on a large-scale system to investigate the performance using a 3-diode model under different irradiation and temperature.The experimental data from the PV array is used in this case study.Three strings are linked in parallel with six strings in the section of the PV array that is being used per string, there are PV modules.The PV module's identifier is a mono-crystalline GL-M100 made up of 36 cells in a single crystal series.Temperature and irradiance are the I-V characteristics.The PROVA1011 I-V tester was used to measure the results.The PV module's electrical properties are accessible in 37 .
To demonstrate, a single-diode model was used.To investigate the performance of the suggested algorithm, the approach has been put into practice on a wide scale.The experimental values of PROVA1011 are also taken into consideration to evaluate the iv characteristics under real-time changes in irradiation and temperature.The graph in Fig. 11.demonstrates the accuracy of estimated values using the DSO optimization technique with the experimental curves.A comparison with the literature 38 is carried out to demonstrate the effectiveness of the DSO algorithm.RMSE estimated using the DSO approach shows superior results as compared with recent literature.This work aims for reliable estimation of parameters since it accounts for all the changes concerning irradiation and temperature.The detailed parameters estimation of the 3-diode model solar system is given in Table 4.

Conclusion
Three-diode modeling poses a complexity due to the inclusion of various parameters.Single and double-diode models are most commonly used to estimate the five and seven parameters due to simplicity.An attempt towards addressing the complex Two cases with three different commercial solar cells/modules were considered to test the accuracy of the result.Real-time experimental data under changing irradiation and temperature conditions are also considered to check the effectiveness of the proposed DSO algorithm.Two cases with three different commercial solar cells/modules were considered to test the accuracy of the result.Real-time experimental data under changing irradiation and temperature conditions are also considered to check the effectiveness of the proposed DSO algorithm.A comprehensive comparison of recent Meta-heuristic algorithms with recent literature is illustrated to prove the accuracy and reliability of the proposed work.Despite modeling complexities, this work ensures optimal results with good precision.This DSO can further be used to solve complex multi-objective optimization problems in fields of renewable energy, power systems, and smart grids.This research work enables budding researchers who study the impact of partial shading and charming, as it accounts for various parameters and constraints.A high level of precision between the estimated values and experimental values indicates the robustness of modeling and its adaptation to the DSO algorithm.The obtained result proves the superiority of the algorithm in extracting the PV parameters accurately.

Figure 1 .
Figure 1.Parameter extraction methods and modeling approaches.

Figure 4 .
Figure 4. Flow chart depicting process flow diagram of DSO.

Figure 5 .
Figure 5.The IV performance characteristics of RTC France Cell with experimental curves overlapping with estimated values.

Figure 6 .
Figure 6.The PV performance characteristics of Photo-watt PWP-201 Cell with experimental curves overlapping with estimated values.

Figure 11
Figure 11 presents the best solution of the objective function for two different PV Cells.It is clear from the figure that the solution with the least error is achieved with a minimum no of runs.Table 3 demonstrates the results obtained from the DSO algorithm for the 3-diode model in comparison with eight recent competitive Fig.11.Presents the best solution of the objective function for two different PV Cells.It is clear from the figure that the solution with the least error is achieved with a minimum no of runs.Table3demonstrates the results obtained from the DSO algorithm for the 3-diode model in comparison with eight recent competitive algorithms.In literature[31][32][33][34][35][36] parameters are extracted for single and double diode models only.The proposed work estimates 15 parameters of three diode model and comparison is done considering 2 diodes, and 9-parameters.It's worth

Figure 7 .
Figure 7. Best run with least RMSE for RTC France Cell.

Figure 8 .
Figure 8.The IV performance characteristics of Photo-watt PWP-201 Cell with experimental curves overlapping with estimated values.

Figure 9 .
Figure 9.The PV performance characteristics of Photo-watt PWP-201 Cell with experimental curves overlapping with estimated values.

Figure 10 .
Figure 10.Best run with least RMSE for Photo-watt PWP-201 Cell.

Figure 11 .
Figure 11.Best results for different runs in terms of RMSE for Photo-watt PWP-201 Cell.

Table 1 .
Data-sheet values of commercial solar cells.and PWP-201 with 36 cells at Irradiation of 1000 w/m 2 and temperature of 45 °C using Datasheet values.The Data sheet values specified by the manufacturer are presented in the Table

Table . 2
.. Data-sheet values of commercial solar cells.

Table 3 .
Comparison of estimated parameter of Three diode model of Photo Watt PWP-201 with literature 31 .

Table 4 .
Parameters estimated for three diode models with different irradiation and temperature.